The known 1,4:3,6-dianhydrohexitols are in particular: isosorbide, isomannide and isoidide of formula:

Also known are derivatives of isosorbide, isomannide and isoidide wherein the reactive —OH functions are replaced by reactive amine, acid or ether functions.
is an example of an ether derivative of isosorbide. DMI is a recommended solvent in pharmaceutical and cosmetic compositions such as self-tanning, oral hygiene or anti-acne compositions, skin care creams, ointments and lotions. DMI is also a viscosity control agent. It can be used as a fluxing agent for bitumens.
The use of DMI in many fields other than the pharmaceutical and cosmetic industry is in particular described in the Applicant's international applications WO 2006/120342 and WO 2006/120343.
DMI is typically prepared by methylation of isosorbide with a methylating agent such as dimethyl sulfate or methyl chloride, in the presence of an alkaline agent such as soda. For economic reasons, methyl chloride is a particularly advantageous methylating agent. It is in fact available on the market in large quantities and at a cost lower than that of the brominated or iodinated equivalents. Thus the patent application EP 0 092 998 describes the methylation of isosorbide with methyl chloride (MeCl) in the presence of sodium or potassium hydroxide. The reaction described is performed in a water/aprotic organic solvent (DMSO or toluene) dispersion, bubbling in the gaseous methylating agent.
Although it affords high yields of DMI (90-95%), this methylation in an aqueous medium nonetheless poses the following problems:    (i) hydrolysis of the methylating agent. In fact, this undesirable side reaction reduces the ratio [MeCl bound/MeCl introduced], hereinafter referred to as the MeCl binding ratio, and leads to the formation of considerable quantities of salts, generally sodium chloride or potassium chloride, which must be removed at the end of the process    (ii) gaseous reagent difficult to use    (iii) toxicity of the methyl chloride reagent    (iv) toxicity of the solvent (DMSO or toluene).
The use of dialkyl carbonate (dimethyl or diethyl) to obtain DMI from isosorbide does not involve these disadvantages (i), (ii), (iii) and (iv). This methylating agent is used both as reagent and “green” solvent. It is used in the presence of a basic catalyst. The reaction takes place at high temperatures and pressures and utilizes only one methyl group of the dimethyl carbonate, which adversely affects the economics of the process (U.S. Pat. No. 4,770,871; WO 2009/120703). In particular, this latter international patent application WO 2009/120703 describes a process for etherification of the dianhydrohexitol sugars in the presence of an O-alkylating agent which is a dialkyl carbonate.
There is thus a need for a clean method for synthesis of DMI and more generally of di, without generation of salts in particular, with an inexpensive and efficient methylating agent (without loss of carbon).
It must be noted that the prior art does not meet this need.